To add to what has already been mentioned about the textile industry, the Power Loom was invented in 1785 by Edmund Cartwright. This invention allowed the weavers to keep up the spinning jenny.
In his novel Tess of the D'Ubervilles, Thomas Hardy writes of the tremendous effect of the Industrial Revolution in the English countryside. When the railroad came through England, the area where Tess lived changed from medieval life to contemporary. Machines such as the threshing machine made farm workers unnecessary. Both the trains and the threshing machines were powered by steam. ( Trains could also run on coal.)
Two very important inventions for sailors were the sextant (1757)which could measure longitude and latitude and the marine chronometer for measuring longitude (1761)
I personally think that the impact of the Spinning Jenny as highlighted above by amy-lepore is incredibly important for being part of the industrial revolution that changed the face of Europe as we know it. In addition, as other editors have highlighted, the steam engine likewise changed geography and our understanding of travel drastically.
This is definitely a matter of opinion, but a few more to add to your list of possibles are:
1755--the first English Dictionary (that may not seem like a huge accomplishment, but it did wonders in streamlining spelling and catapulting the academic world into a new era).
1764--the spinning jenny (a wonder for the textile industry and the housewife)
1774--the electric telegraph (communication advancement)
While I'm no expert in European inventions after 1750, it does seem as if there are a few categories of things you can explore to develop your own opinion. Two are mentioned above: medicine and transportation. A third would have to be communication. These three categories are likely to yield some of the most significant inventions, it seems to me.
This is, of course, a matter of opinion.
To me, however, I think that the following things could be seen as some of the most important inventions in Europe:
- Steam engine. This may be the most important. It led to, among other things, the creation of railroads and of powered ships. These two things totally transformed the world, allowing even more efficient expansion by European countries and by the US.
- The Daguerreotype. This early photographic technology allowed people to see images from faraway places as they never could before.
- The smallpox vaccine. This set people on their way to eradicating one of the most terrible diseases in the world.